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Chi-Square Test

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Chi-Square (χ2) Test Used to determine if there is a significant difference between the expected and observed data Null hypothesis: There is NO statistically significant difference between expected & observed data Any differences are due to CHANCE alone

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**Chi-Square (χ2) Formula**

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**How to use the Chi-Square Test**

Determine null hypothesis All frequencies are equal –OR– Specific frequencies given already Use formula to calculate χ2 value: n = # of categories, e = expected, o = observed Find critical value using table (Use p=0.05). degrees of freedom (df) = n – 1 If χ2 < Critical Value, then ACCEPT null hypothesis. Differences in data are due to chance alone. If χ2 > Critical Value, REJECT the null hypothesis: Differences in data are NOT due to chance alone!

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Sample Problem You buy a package of M&Ms from the factory store and find the following: 20 brown, 20 blue, 20 orange, 20 green, and 20 yellow M&Ms. According to the M&M website, each package of candy should have 13% brown, 24% blue, 20% orange, 16% green, 13% red, and 14% yellow M&Ms. You realize you are missing Red M&M’s in your package! Is this acceptable, or did something happen in the factory during the packaging process? Use the Chi-Square Test to answer this question.

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**Warm up – Chi-Square Practice**

A high school, students can choose to enter one of three doors. Custodians noticed that door #3 was always getting broken and suggested that more students use that door because it has a hands- free opener. Science minded students counted the number of students entering each door to see if the custodians were right. Door #1 had 60 students enter Door #2 had 66 students enter Door #3 had 80 students enter Were the custodians’ suspicions supported by the data? Use a Chi- Square Test to support your answer.

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